Vortex Filament Equation and Non-Lightlike Space Curves in Minkowski 3-space
Differential Geometry
2013-10-09 v1 Dynamical Systems
Abstract
In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schr\"odinger equation and non-linear heat system to the vortex filament equation for the binormal motion of non-lightlike curves is shown by use of the parallel frames and their evolution equations.
Keywords
Cite
@article{arxiv.1310.2108,
title = {Vortex Filament Equation and Non-Lightlike Space Curves in Minkowski 3-space},
author = {Nevin Gürbüz and Süleyman Cengiz},
journal= {arXiv preprint arXiv:1310.2108},
year = {2013}
}